Tube lemma
In mathematics, particularly topology, the tube lemma, also called Wallace's theorem, is a useful tool in order to prove that the product of finitely many compact spaces is compact. == Statement == The lemma uses the following terminology: If X {\displaystyle X} and Y {\displaystyle Y} are topological spaces and X × Y {\displaystyle X\times Y} is the product space, endowed with the product topology, a slice in X × Y {\displaystyle X\times Y} is a set of the form { x } × Y {\displaystyle \{x\}\times Y} for x ∈ X {\displaystyle x\in X} .